Accelerometers are sensors that measure acceleration. Accelerometers can be designed to measure rotational or translational acceleration. Vibratory rate gyroscopes are a type of accelerometer in which one or more proof-masses are forced into oscillation and a Coriolis acceleration is detected in response to a rate input. Accelerometers and rate gyroscopes have many uses in many commercial, military, and scientific applications including, but not limited to, inertial navigation, vehicular safety systems such as airbags, ride comfort control, platform stabilization, tilt sensing, vibration monitoring, shock and impact measurement, and weapons fusing.
The heart of a displacement-based accelerometer is a mechanical proof-mass. Under an applied acceleration, this passive mechanical device moves with respect to the substrate. For an accelerometer with a linear suspension, it may be shown that for frequencies below the proof-mass resonant frequency along the sensitive axis, ωn, the displacement of the proof-mass from its nominal position with respect to the substrate is given by 1/ωn2 times the applied acceleration. By measuring the displacement of the proof-mass with an electrical interface, acceleration may be inferred.
A sense-element may be operated either open-loop, or placed into a force-feedback loop. Enclosure of a sense-element in a force-feedback loop is commonly called force-balancing or force-rebalancing. In the open-loop configuration, the accelerometer output is given by the change in relative displacement of the proof-mass multiplied by the gain of the position sense interface. Often piezoelectric materials, piezoresistive materials, or sense capacitors are used in conjunction with an electrical position-sense interface to detect proof-mass displacements.
In the force-balanced configuration the position-sense interface output is used to feed back a force in a manner that tends to restore the proof-mass to a defined nominal position. Note the accelerometer output is not a quantity representative of position, but rather is a quantity representative of the force necessary to keep the proof mass at its nominal position. Because force-balanced accelerometers maintain small displacements for acceleration inputs within the measuring range, electrostatic nonlinearities due to changes in air gap capacitance are attenuated. Closed-loop operation has been used to provide several advantages that are particularly important for miniature micromachined sensors including improved linearity, increased dynamic range, and extended bandwidth. In addition, since the output is the applied force, not displacement, the output typically is less sensitive to device dimensions, such as spring width, making the sensor typically less sensitive to variations in manufacturing. Sense capacitors or piezoelectric materials are often used to apply feedback forces to the proof mass.
Note force-feedback is not practical or even desirable for many applications, however. As full scale ranges rise above approximately 50G, it becomes increasingly difficult to force balance an accelerometer in a manner such that the feedback loop doesn't saturate, especially if electrostatic forces and low-voltage operation (i.e. 5V or less) are used to apply the restoring force feedback. Alternatively, when an application requires a low-cost, small, or simple accelerometer, the increased circuit area or added complexity may preclude usage of force-balanced topologies. Although some applications may not allow for force balancing, many of these same target applications will require good input-output linearity and a wide dynamic range that force balancing provides. Furthermore, it is often desirable that the sensor include a differential sense interface for improved rejection of undesired disturbances, such as power supply fluctuations.
A substantially parallel-plate capacitor is defined here as a capacitor having a nonlinear relationship between capacitance and displacement along an axis of sensitivity; a significant component of capacitance being described by the equation K/g, where K is a geometrically determined constant and g is a characteristic distance between sense electrodes as measured orthogonally from the face of one sense electrode. Substantially parallel-plate capacitors may be advantageous in many applications because in addition to a typically higher sensitivity to changes in air-gap, substantially parallel-plate capacitors typically provide significantly higher air-damping than alternative configurations such as interdigitated comb fingers (see for example Tang et al U.S. Pat. No. 5,025,346 issued Jun. 18, 1991). Higher air damping is beneficial to many applications where underdamped mechanical resonances are undesirable including, but not limited to, accelerometers and open-loop actuators.
FIG. 1 shows an example of a substantially parallel-plate capacitor with conductive electrodes 40 and 41, each electrode having an area A equal to plate length/multiplied by plate width w. When the length and width are substantially greater than the separation gap g, the capacitance, C, between the two plates may be approximated by:C≈ε0A/gAs either plate width or plate length approach the gap dimension, the above approximation becomes less accurate, since fringing fields comprise a larger percentage of capacitance. Note that the capacitance is highly nonlinear with a 1/g dependence. To attain a representation of position that is linear, a position sense interface must account for this nonlinearity.
A sense capacitor is defined, within the scope of this document, as one or more substantially parallel-plate capacitors connected in parallel. Note, in certain applications, a substantially parallel-plate capacitor may have gasses between electrodes at a reduced pressure, or vacuum, for lower mechanical damping. Furthermore, substantially parallel-plate capacitors may include between the electrodes any of a number of gasses including, but not limited to, one or more of the following: nitrogen, argon, hydrogen, helium, oxygen, or other gasses or combination of gasses.
Often a position sense interface requires a pair of sense capacitors that change oppositely in value for a displacement in the same direction. A pair of sense capacitors that change in this manner provide a degree of symmetry that may result in reduced offset and drift over temperature. Furthermore, a pair of sense capacitors may enable the use of differential circuit techniques that reject certain environmental noise sources such as power supply ripple.